Component groups of unipotent centralizers in good characteristic

2002/04/30 by George J. McNinch, Eric Sommers · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research #math.GR #math.RT #msc:20G05 #msc:20Gxx

paper · pdf · doi:10.1016/s0021-8693(02)00661-0

published as Journal of Algebra 260 (2003) 323-337 · 13 pages; AMS LaTeX. This is the final version; it will appear in the Steinberg birthday volume of the Journal of Algebra. This version corrects an oversight pointed out by the referee; see Prop 23

arxiv created 2002/08/13 · openalex publication_date 2003/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let G be a connected, reductive group over an algebraically closed field of good characteristic. For u in G unipotent, we describe the conjugacy classes in the component group A(u) of the centralizer of u. Our results extend work of the second author done for simple, adjoint G over the complex numbers. When G is simple and adjoint, the previous work of the second author makes our description combinatorial and explicit; moreover, it turns out that knowledge of the conjugacy classes suffices to determine the group structure of A(u). Thus we obtain the result, previously known through case-checking, that the structure of the component group A(u) is independent of good characteristic.

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